🌀 Viscoelastic Fluid

About this simulation

Viscoelastic materials behave like a spring and a syrup at the same time: they store energy elastically and dissipate it viscously. This simulation lets you poke an interactive spring-dashpot blob and watch rheological models — Maxwell, Kelvin-Voigt and the Standard Linear Solid — predict stress relaxation, creep and dynamic moduli. The same physics governs Silly Putty, molten plastics, asphalt, biological tissue and the polymer melts behind every plastic product you own.

How it works

• A 10×10 particle grid is linked by Maxwell spring-dashpot bonds, each tracking a viscous extension that slowly relaxes.
• Bond forces are integrated in an overdamped scheme; bond colour maps the local stress magnitude (blue = low, red = high).
• The right panel plots the chosen analytical test — relaxation G(t), creep J(t) or a frequency sweep of G′(ω) and G″(ω).
• Switching the model rewires the springs and dashpots from series (Maxwell) to parallel (Kelvin-Voigt) to a combined SLS network.

Key equations

De = tauR / t_obs, tauR = eta / G0 — the Deborah number De compares the material relaxation time tauR (viscosity η over modulus G₀) with the observation time. De > 1 looks solid-like; De < 1 flows like a liquid.

Controls

• Model — choose Maxwell, Kelvin-Voigt or Standard Linear Solid.
• Modulus G₀ — elastic stiffness of the springs (kPa).
• Viscosity η — dashpot resistance to flow (kPa·s).
• SLS spring ratio α — plateau-to-total stiffness split for the SLS model.
• Test tabs — Stress Relaxation, Creep, Frequency Sweep.
• Presets — Silly Putty, Silicone Gel, Polymer Melt, Ideal Spring, Ideal Dashpot.
• Blob canvas — click-drag a node to deform the material.

Did you know?

The Deborah number is named after the biblical prophetess Deborah, who sang "the mountains flowed before the Lord" — coined by rheologist Markus Reiner to make the point that, given enough time, even mountains behave like fluids.